"We talked about different vectors of co-operation - how to achieve real peace and guarantee Ukraine's security," Zelenskiy wrote of their meeting in Kyiv on the Telegram messaging app.
Discussions included "strong bilateral agreements on joint production of drones and weapons, which we have proposed to America. We are counting on a positive reaction from the US".
The two also spoke of "pressure on the Russians and what we can do together with our partners in tariff and sanctions policy so that we can meet at the leadership level as soon as possible and end this war".
Ukrainian drones attacked a training centre at the Zaporizhzhia Nuclear Power Plant on Thursday, the Kremlin-installed administration of the Russia-held plant in Ukraine said.
There were no casualties and information on potential damage was being clarified, the plant administration said.
Reuters could not independently verify the report.
Russian forces seized the Zaporizhzhia plant in the first weeks of Russia's February 2022 invasion of Ukraine.
Each side regularly accuses the other of firing or taking other actions that could trigger a nuclear accident.
Poland said on Thursday the United Nations Security Council will hold an emergency meeting to discuss drone incursions into its airspace which the Polish president described as an attempt by Russia to test the NATO military alliance's response.
Poland also banned drone flights along its eastern borders with Belarus and Ukraine, and limited small air traffic there, after shooting down what it said were Russian drones that violated its airspace on Wednesday.
Poland was backed by its NATO allies in shooting down the drones - the first time a member of the military alliance is known to have fired shots during Russia's war in Ukraine - and Germany said on Thursday it would strengthen its commitment to NATO's eastern border in response to the incursions.
Russia said it had not intended to hit any targets in Poland and that it would make no further comment on the incident.
A senior NATO commander said it was not yet known whether the drone incursions were intentional.
"This Russian provocation, as the generals and our soldiers are well aware, was nothing more than an attempt to test our capabilities, our ability to respond," Polish President Karol Nawrocki told soldiers on Thursday.
The foreign ministry said the UN Security Council would meet at Poland's request but did not say when.
The UN did not immediately comment but Slovenia, Denmark, Greece, France and the United Kingdom have asked the Security Council to meet on Friday, diplomats said on Wednesday.
